The level of nitrogen oxides (NOX) in the exhaust after 50,000 miles or fewer of driving of cars of a particular model varies Normally with mean 0.02 g/mi and standard deviation 0.01 g/mi. A company has 81 cars of this model in its fleet. What is the level L such that the probability that the average NOX level x for the fleet is greater than L is only 0.01? (Hint: This requires a backward Normal calculation. Round your answer to three decimal places.)

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ChiKesselman ChiKesselman · Answer 1 · 2020-03-12T08:22:48+01:00

Answer:

For a level of 0.0174 or more of nitrogen oxide, the probability of fleet is 0.01.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 0.02 g/mi

Standard Deviation, σ = 0.01 g/mi

Sample size, n = 81

We are given that the distribution of level of nitrogen oxides is a bell shaped distribution that is a normal distribution.

Standard error due to sampling:

[tex]=\dfrac{\sigma}{\sqrt{n}} = \dfrac{0.01}{\sqrt{81}} = 0.0011[/tex]

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

We have to find the value of x such that the probability is 0.01

P(X > x)

[tex]P( X > x) = P( z > \displaystyle\frac{x - 0.02}{0.0011})=0.01[/tex]

[tex]= 1 -P( z \leq \displaystyle\frac{x - 0.02}{0.0011})=0.01 [/tex]

[tex]=P( z \leq \displaystyle\frac{x - 0.02}{0.0011})=0.99[/tex]

Calculation the value from standard normal z table, we have,

[tex]\displaystyle\frac{x - 0.02}{0.0011} = -2.326\\\\x = 0.0174[/tex]

For a level of 0.0174 or more of nitrogen oxide, the probability of fleet is 0.01.